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Block #909,081

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/25/2015, 7:11:20 AM Β· Difficulty 10.9345 Β· 5,905,153 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
e9a5a86f6c3499f45d697fa883f8e0d64a40719bc954847dd4928b9fcfcfcaf6
View on Chainz β†—

Height

#909,081

Difficulty

10.934457

Transactions

2

Size

11.26 KB

Version

2

Bits

0aef3892

Nonce

1,317,990,012

Timestamp

1/25/2015, 7:11:20 AM

Confirmations

5,905,153

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d6419b3fcacd5441b74051e70e200ad790130886e769c937919c2727f33268e4
Transactions (2)
Coinbase4faf2375ef3cc5…bf18c68be795a1
1 in β†’ 1 out8.4700 XPM116 B
ANSXnLY2…Sd25TjkD
b8bec653c7e399…0de059f3c49228
76 in β†’ 2 out7348.9734 XPM11.06 KB
AcAFW717…V1pWEX3JAYMabPpJ…Qt84CChP
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.548 Γ— 10⁹⁷(98-digit number)
15484404431481726482…54907827617145984001
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.548 Γ— 10⁹⁷(98-digit number)
15484404431481726482…54907827617145984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.096 Γ— 10⁹⁷(98-digit number)
30968808862963452965…09815655234291968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.193 Γ— 10⁹⁷(98-digit number)
61937617725926905931…19631310468583936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.238 Γ— 10⁹⁸(99-digit number)
12387523545185381186…39262620937167872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.477 Γ— 10⁹⁸(99-digit number)
24775047090370762372…78525241874335744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.955 Γ— 10⁹⁸(99-digit number)
49550094180741524745…57050483748671488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.910 Γ— 10⁹⁸(99-digit number)
99100188361483049490…14100967497342976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.982 Γ— 10⁹⁹(100-digit number)
19820037672296609898…28201934994685952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.964 Γ— 10⁹⁹(100-digit number)
39640075344593219796…56403869989371904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.928 Γ— 10⁹⁹(100-digit number)
79280150689186439592…12807739978743808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.585 Γ— 10¹⁰⁰(101-digit number)
15856030137837287918…25615479957487616001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,757,943 XPMΒ·at block #6,814,233 Β· updates every 60s
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